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Spin Study at JLab from Longitudinal to

Transverse

- J. P. Chen, Jefferson Lab
- Berkeley Summer Spin Program, 2009, LBNL,

California

- Introduction
- Longitudinal and transverse spin
- Selected results from JLab
- Recently completed and planned measurements
- 12 GeV plan

Strong Interaction and QCD

- Strong interaction, running coupling 1
- -- QCD accepted theory for strong

interaction - -- asymptotic freedom (2004 Nobel)
- perturbation calculation works at

high energy - -- interaction significant at intermediate

energy - quark-gluon correlations
- -- interaction strong at low energy

(nucleon size) - confinement
- theoretical tools
- pQCD, OPE, Lattice QCD, ChPT,
- A major challenge in fundamental physics
- Understand QCD in strong interaction

region - ? Study and understand nucleon structure

as

E

Nucleon Structure and Sum Rules

- Global properties and structure
- Mass 99 of the visible mass in

universe - 1 GeV, but u/d quark mass

only a few MeV each! - Momentum quarks carry 50
- Spin ½, quarks contribution 30

Spin Sum Rule - Magnetic moment large part anomalous,

gt150 GDH Sum Rule - Axial charge

Bjorken Sum Rule - Angular momentum

Jis Sum Rule - Polarizabilities (Spin, Color)
- Tensor charge

Three Decades of Spin Structure Study

- 1980s EMC (CERN) early SLAC
- quark contribution to proton spin is very

small - DS (12-9-14) ! spin

crisis - (Ellis-Jaffe sum rule violated)
- 1990s SLAC, SMC (CERN), HERMES (DESY)
- DS 20-30
- the rest gluon and quark orbital angular

momentum - A0 (light-cone) gauge (½)DS Lq DG

Lg1/2 (Jaffe) - gauge invariant (½)DS

Lq JG 1/2 (Ji) - A new decomposition (X. Chen, et. al)
- Bjorken Sum Rule verified to lt10 level
- 2000s COMPASS (CERN), HERMES, RHIC-Spin, JLab,

- DS 30 DG probably small, orbital angular

momentum probably significant - Transversity, Transverse-Momentum Dependent

Distributions - Generalized Parton Distributions

Unpolarized and Polarized Structure functions

Parton Distributions (CTEQ6 and DSSV)

Polarized PDFs

Unpolarized PDFs

CTEQ6, JHEP 0207, 012 (2002)

DSSV, PRL101, 072001 (2008)

Jefferson Lab Experimental Halls

6 GeV polarized CW electron beam Pol85, 180mA

Will be upgraded to 12 GeV by 2014

HallA two HRS Hall

BCLAS Hall C HMSSOS

Jefferson Lab Hall A Experimental Setup for

inclusive polarized n (3He) Experiments

Hall A polarized 3He target

- longitudinal,
- transverse and vertical
- Luminosity1036 (1/s)
- (highest in the world)
- High in-beam polarization
- gt 65
- Effective polarized
- neutron target
- 12 completed experiments
- 1 are currently running
- 6 approved with 12 GeV (A/C)

15 uA

Hall B/C Polarized proton/deuteron target

- Polarized NH3/ND3 targets
- Dynamical Nuclear Polarization
- In-beam average polarization
- 70-90 for p
- 30-40 for d
- Luminosity up to 1035 (Hall C)
- 1034 (Hall B)

JLab Spin Experiments

- Results
- Moments Spin Sum Rules and Polarizabilities
- Higher twists g2/d2
- Quark-Hadron duality
- Spin in the valence (high-x) region
- Just completed
- d2p (SANE) and d2n
- Transversity (n)
- Planned
- g2p at low Q2
- Future 12 GeV
- Inclusive A1/d2,
- Semi-Inclusive Transversity, TMDs,

Flavor-decomposition - Review Sebastian, Chen, Leader, arXiv0812.3535,

PPNP 63 (2009) 1

Longitudinal Spin (I)

Spin in Valence (high-x) Region

Valence (high-x) A1p and A1n results

Hall A E99-117, PRL 92, 012004 (2004)

PRC 70, 065207 (2004)

Hall B CLAS, Phys.Lett. B641 (2006) 11

pQCD with Quark Orbital Angular Momentum

F. Yuan, H. Avakian, S. Brodsky, and A. Deur,

arXiv0705.1553

Inclusive Hall A and B and Semi-Inclusive Hermes

BBS

BBSOAM

Projections for JLab at 11 GeV

A1p at 11 GeV

Flavor decomposition with SIDIS

Du and Dd at JLab 11 GeV

Polarized Sea

Longitudinal Spin (II)

Quark Hadron Duality in Spin Strcuture Function

Duality in Spin-Structure Hall A E01-012 Results

A13He (resonance vs DIS)

- g1/g2 and A1/A2 (3He/n) in resonance region,
- 1 lt Q2 lt 4 GeV2
- Study quark-hadron duality in spin structure.
- ltResonancesgt ltDISgt ?
- PRL 101, 1825 02 (2008)

Duality in Spin-Structure Partial Moment Results

G1 resonance comparison with pdfs

Spin Sum Rules Zeroth Moments

Sum Rules

Moments of Spin Structure Functions

?

Global Property

Bjørken Sum Rule

gA axial vector coupling constant from

neutron b-decay CNS Q2-dependent QCD

corrections (for flavor non-singlet)

- A fundamental relation relating an integration of

spin structure functions to axial-vector coupling

constant - Based on Operator Product Expansion within QCD or

Current Algebra - Valid at large Q2 (higher-twist effects

negligible) - Data are consistent with the Bjørken Sum Rule at

5-10 level

Gerasimov-Drell-Hearn Sum Rule Circularly

polarized photon on longitudinally polarized

nucleon

- A fundamental relation between the nucleon spin

structure and its anomalous magnetic moment - Based on general physics principles
- Lorentz invariance, gauge invariance ? low

energy theorem - unitarity ? optical theorem
- casuality ? unsubtracted dispersion relation
- applied to forward Compton

amplitude - First measurement on proton up to 800 MeV (Mainz)

and up to 3 GeV (Bonn) - agree with GDH with assumptions for

contributions from un-measured regions - New measurements from LEGS, MAMI(2),

Generalized GDH Sum Rule

- Many approaches Anselmino, Ioffe, Burkert,

Drechsel, - Ji and Osborne (J. Phys. G27, 127, 2001)
- Forward Virtual-Virtual Compton Scattering

Amplitudes S1(Q2,n), S2(Q2, n) - Same assumptions no-subtraction dispersion

relation - optical theorem
- (low energy

theorem) - Generalized GDH Sum Rule

Connecting GDH with Bjorken Sum Rules

- Q2-evolution of GDH Sum Rule provides a bridge

linking strong QCD to pQCD - Bjorken and GDH sum rules are two limiting cases
- High Q2, Operator Product Expansion

S1(p-n) gA ? Bjorken - Q2 ? 0, Low Energy Theorem

S1 k2 ? GDH - High Q2 (gt 1 GeV2) Operator Product Expansion
- Intermediate Q2 region Lattice QCD calculations
- Low Q2 region (lt 0.1 GeV2) Chiral Perturbation

Theory - Calculations HBcPT Ji, Kao, Osborne,

Spitzenberg, Vanderhaeghen - RBcPT Bernard, Hemmert,

Meissner - Reviews Theory Drechsel, Pasquini,

Vanderhaeghen, Phys. Rep. 378,99 (2003) - Experiments Chen, Deur,

Meziani, Mod. Phy. Lett. A 20, 2745 (2005)

JLab E94-010 (Hall A) Neutron spin structure

moments and sum rules at Low Q2

GDH integral on neutron

- Q2 evolution of neutron spin structure moments
- (sum rules) with pol. 3He
- transition from quark-gluon to hadron
- Test cPT calculations
- Results published in several PRL/PLBs

Q2

PRL 89 (2002) 242301

First Moment of g1p and g1n G1p and G1n

Test fundamental understanding

ChPT at low Q2, Twist expansion at high Q2,

Future Lattice QCD

G1p

G1n

E94-010, from 3He, PRL 92 (2004) 022301

E97-110, from 3He, preliminary EG1a, from d-p

EG1b, arXiv0802.2232 EG1a, PRL 91, 222002

(2003)

G1 of p-n

EG1b, PRD 78, 032001 (2008) E94-010 EG1a PRL

93 (2004) 212001

Effective Strong Coupling

A new attempt at low Q2

Experimental Extraction from Bjorken Sum

The strong coupling constant from pQCD

as (Q) is well defined in pQCD at large Q2. Can

be extracted from data (e.g. Bjorken Sum

Rule). Not well defined at low Q2, diverges

at LQCD

Definition of effective QCD couplings

G. Grunberg, PLB B95 70 (1980) PRD 29 2315

(1984) PRD 40 680(1989).

Prescription Define effective couplings from a

perturbative series truncated to the first term

in as.

Generalized Bjorken sum rule

Use

to define an effective

asg1. Process dependent. But can be related

through Commensurate scale relations S.J.

Brodsky H.J Lu, PRD 51 3652 (1995)? S.J.

Brodsky, G.T. Gabadadze, A.L. Kataev, H.J Lu, PLB

372 133 (1996)? Extend it to low Q2 down to 0

include all higher twists.

Effective Coupling Extracted from Bjorken Sum

A. Deur, V. Burkert, J. P. Chen and W. Korsch

PLB 650, 244 (2007) and PLB 665, 349 (2008)

as/p

Comparison with theory

?

Fisher et al. Bloch et al. Maris-Tandy Bhagwat et

al. Cornwall Godfrey-Isgur Constituant

Quark Model Furui

Nakajima Lattice

Schwinger -Dyson

Furui Nakajima

Transverse Spin (I) Inclusive

g2 Structure Function and Moments Burkhardt -

Cottingham Sum Rule

g2 twist-3, q-g correlations

- experiments transversely polarized target
- SLAC E155x, (p/d)
- JLab Hall A (n), Hall C (p/d)
- g2 leading twist related to g1 by

Wandzura-Wilczek relation

- g2 - g2WW a clean way to access twist-3

contribution - quantify q-g correlations

Precision Measurement of g2n(x,Q2) Search for

Higher Twist Effects

- Measure higher twist ? quark-gluon correlations.
- Hall A Collaboration, K. Kramer et al., PRL 95,

142002 (2005)

BC Sum Rule

0ltXlt1 Total Integral

P

Brawn SLAC E155x Red Hall C RSS Black Hall A

E94-010 Green Hall A E97-110 (preliminary) Blue

Hall A E01-012 (very preliminary)

N

BC Measlow_xElastic

Meas Measured x-range

3He

low-x refers to unmeasured low x part of the

integral. Assume Leading Twist Behaviour

Elastic From well know FFs (lt5)

BC Sum Rule

P

BC satisfied w/in errors for JLab Proton 2.8?

violation seen in SLAC data

N

BC satisfied w/in errors for Neutron

(But just barely in vicinity of Q21!)

3He

BC satisfied w/in errors for 3He

BC Sum Rule

What can BC tell us about Low-X?

P

N

Unmeasured Low-X

DIS -(RESELAS)

3He

Spin Polarizabilities

Higher Moments of Spin Structure Functions at Low

Q2

Higher Moments Generalized Spin Polarizabilities

- generalized forward spin polarizability g0
- generalized L-T spin polarizability dLT

Neutron Spin Polarizabilities

- dLT insensitive to D resonance
- RB ChPT calculation with resonance for g0 agree

with data at Q20.1 GeV2 - Significant disagreement between data and both

ChPT calculations for dLT - Good agreement with MAID model predictions
- g0

dLT

E94-010, PRL 93 (2004) 152301

Q2

Q2

CLAS Proton Spin Polarizability

g0p

g0p Q6

- EG1b, Prok et al.
- arXiv0802.2232
- Large discrepancies with ChPT!
- Only longitudinal data, model for transverse

(g2) - g0 sensitive to resonance

Summary of Comparison with cPT

- IAn G1P

G1n G1p-n

g0p g0n dLTn - Q2 (GeV2) 0.1 0.1 0.05 0.1 0.05

0.16 0.05 0.05 0.1 0.1 - HBcPT poor poor good poor good good

good bad poor bad - RBcPT/D good fair fair fair good

poor fair bad good bad - dLT puzzle dLT not sensitive to D, one of the

best quantities to test cPT, - it disagrees with neither

calculations by several hundred ! - A challenge to cPT theorists.
- Very low Q2 data g1/g2 on n(3He) (E97-110)
- g1 on p and d

available soon (EG4) - Recently approved g2 on proton E08-027

New Experiment Proton g2 and ?LT

E08-027 A- rating by PAC33

K. Slifer, A. Camsonne, ,J. P. Chen

- Critical input to Hydrogen Hyperfine Calculations
- Violation of BC Sum Rule suggested at large Q2
- State-of-Art ?PT calcs fail dramatically for ?LT

Septa Magnets for low Q2 Transverse bPolarized

Proton Target

n

?LT Spin Polarizability

BC Sum Rule

Color Polarizabilities

Higher Moments of Spin Structure Functions at

High Q2

Color Polarizability (or Lorentz Force) d2

- 2nd moment of g2-g2WW
- d2 twist-3 matrix element

d2 and g2-g2WW clean access of higher twist

(twist-3) effect q-g correlations Color

polarizabilities cE,cB are linear combination of

d2 and f2 Provide a benchmark test of Lattice

QCD at high Q2 Avoid issue of low-x

extrapolation Relation to Sivers and other

TMDs?

Measurements on neutron d2n (Hall A and SLAC)

d2(Q2)

BRAND NEW DATA!

Very Preliminary

Proton MAID Model

RED RSS. (Hall C, NH3,ND3)

BLUE E01-012. (Hall A, 3He)

Neutron

GREEN E97-110. (Hall A, 3He)

stat only

d2(Q2)

E08-027 g2p

SANE

6 GeV Experiments Sane just completed in Hall

C g2p in Hall A, 2011

projected

d2n just completed in Hall A

Planned d2n with JLab 12 GeV

- Projections with 12 GeV experiments
- Improved Lattice Calculation (QCDSF,

hep-lat/0506017)

Color Polarizabilities

f2 Extraction and Color Polarizabilities

- JLab world n data,
- m4 (0.019-0.024)M2
- Twist-4 term
- m4 (a24d24f2)M2/9
- extracted from m4 term f2

0.034-0.005-0.043 - f2 can be measured from g3
- Color polarizabilities
- cE 0.033-0.029
- cB -0.001-0.016
- Proton and p-n
- f2 -0.160-0.179 (p),
- -0.136-0.109 (p-n)

PLB 93 (2004) 212001

Transverse Spin (II) Single Spin Asymmetries in

SIDIS

Transversity and TMDs

Transversity

- Three twist-2 quark distributions
- Momentum distributions q(x,Q2) q?(x) q?(x)
- Longitudinal spin distributions ?q(x,Q2) q?(x)

- q?(x) - Transversity distributions dq(x,Q2) q-(x) -

q-(x) - It takes two chiral-odd objects to measure

transversity - Semi-inclusive DIS
- Chiral-odd distributions function (transversity)
- Chiral-odd fragmentation function (Collins

function) - TMDs (without integrating over PT)
- Distribution functions depends on x, k- and Q2

dq, f1T- (x,k- ,Q2), - Fragmentation functions depends on z, p- and Q2

D, H1(x,p- ,Q2) - Measured asymmetries depends on x, z, P- and Q2

Collins, Sivers, - (k-, p- and P- are related)

Leading-Twist TMD Quark Distributions

Nucleon

Unpol.

Trans.

Long.

Quark

Unpol.

Long.

Trans.

Current Status

- Large single spin asymmetry in pp-gtpX
- Collins Asymmetries
- - sizable for proton (HERMES and COMPASS)
- large at high x, p- and p has

opposite sign - unfavored Collins fragmentation as large

as favored (opposite sign)? - - consistent with 0 for deuteron (COMPASS)
- Sivers Asymmetries
- - non-zero for p from proton (HERMES),

consistent with zero (COMPASS)? - - consistent with zero for p- from proton and

for all channels from deuteron - - large for K ?
- Very active theoretical and experimental study
- RHIC-spin, JLab (Hall A 6 GeV, CLAS12,

HallA/C 12 GeV), Belle, FAIR (PAX) - Global Fits/models by Anselmino et al., Yuan et

al. and - First neutron measurement from Hall A 6 GeV

(E06-010)

E06-010 Single Target-Spin Asymmetry in

Semi-Inclusive n?(e,e'p/-) Reaction on a

Transversely Polarized 3He Target

First neutron measurement 7 PhD

Students Completed data taking in Feb. Exceeded

PAC approved goal

Collins

Sivers

Hall-A Transversity

en?epX

en?eKX

Polarized 3He effective polarized neutron

target World highest polarized luminosity

1036 New record in polarization gt70 without

beam 65 in beam and with spin-flip (proposal

42)

HRSL for hadrons (p- and K-), new RICH

commissioned BigBite for electrons, 64 msr,

detectors performing well

Target Performance

- Online preliminary EPR/NMR analysis shows a

stable 65 polarization with 15 mA beam and 20

minute spin flip

Online Preliminary

Projections of g1T

- First Neutron (3He) Measurement
- With Fast Beam Helicity Flip (30Hz)
- Projected Uncertainties (Stat. Only)
- 2.3 at low x
- 3.4 at high x

Precision Study of Transversity and TMDs

- From exploration to precision study
- Transversity fundamental PDFs, tensor charge
- TMDs provide 3-d structure information of the

nucleon - Learn about quark orbital angular momentum
- Multi-dimensional mapping of TMDs
- 3-d (x,z,P- )
- Q2 dependence
- Multi-facilities, global effort
- Precision ? high statistics
- high luminosity and large acceptance

Add new hall

12

6 GeV CEBAF

11

12 GeV Upgrade Kinematical Reach

- Reach a broad DIS region
- Precision SIDIS for transversity and TMDs
- Experimental study/test of factorization
- Decisive inclusive DIS measurements at high-x
- Study GPDs

Solenoid detector for SIDIS at 11 GeV

Proposed for PVDIS at 11 GeV

GEMs

3-D Mapping of Collins/Siver Asymmetries at JLab

12 GeV With A Large Acceptance Solenoid Detector

- Both p and p-
- For one z bin
- (0.5-0.6)
- Will obtain 4
- z bins (0.3-0.7)
- Upgraded PID for K and K-

3-D Projections for Collins and Sivers Asymmetry

(p)

Discussion

- Unprecedented precision 3-d mapping of SSA
- Collins and Sivers
- p, p- and K, K-
- Study factorization with x and z-dependences
- Study PT dependence
- Combining with CLAS12 proton and world data
- extract transversity and fragmentation functions

for both u and d quarks - determine tensor charge
- study TMDs for both valence and sea quarks
- study quark orbital angular momentum
- Combining with world data, especially data from

high energy facilities - study Q2 evolution
- Global efforts (experimentalists and theorists),

global analysis - much better understanding of 3-d nucleon

structure and QCD

Spin Structure with the Solenoid at JLab 12 GeV

- Program on neutron spin structure with polarized

3He and solenoid - Polarized 3He target
- effective polarized neutron
- highest polarized luminosity 1036
- A solenoid with detector package (GEM, EM

calorimeter Cherenkov - large acceptance 700 msr for

polarized (without baffles) - ? high luminosity and large acceptance
- Inclusive DIS improve by a factor of 10-100
- A1 at high-x high precision
- d2 at high Q2 very high precision
- parity violating spin structure g3/g5

first significant measurement - SIDIS improve by a factor of 100-1000
- transversity and TMDs,
- spin-flavor decomposition (2 orders

improvement) - Unpolarized luminosity 5x1038 , acceptance

300 msr (with baffles) - Parity-Violating DIS
- Boer-Mulders function

Single Spin Asymmetries in (Qausi-)Ealstic

Two-photon Exchange and GPDs

E05-015 Target Single Spin Asymmetry Ay

- Inclusive quasi-elastic electron scattering on

vertically polarized 3He target - Target Single Spin Asymmetry Ay0 in one-photon

approximation, two-photon exchange gives non-zero

Ay. - Elastic contribution is well-known,
- inelastic response provides a new way to access

the Generalized Parton Distributions.

E05-015 Projection

- Neutron data provide unique new constraints on

GPDs. - Measurements at Q20.5, 1.0 GeV2
- (and 2 GeV2).
- GPD model prediction and expected uncertainty

(2x10-3) at Q21.0 GeV2. - Data taken competed two weeks ago,
- exceeded approved goal.
- First clear non-zero asymmetry measurement _at_ 10s

level - ? Established quantitatively the
- 2-photon-exchange mechanism.
- ? Established it as a tool to precisely
- probe hadron structure.

Blue curve elastic contrib. Black curve

inelastic contrib. Red point total contrib.

Summary

- Spin structure study full of surprises and

puzzles - A decade of experiments from JLab exciting

results - valence spin structure, quark-hadron duality
- spin sum rules and polarizabilities
- test cPT calculations, ? dLT puzzle
- precision measurements of g2/d2 high-twist
- first neutron transversity measurement
- first quasi-elastic target SSA 2-photon to

probe GPDs - JLab played a major role in recent experimental

efforts - shed light on our understanding of STRONG QCD
- lead to breakthrough?
- Bright future
- complete a chapter in spin structure study with 6

GeV JLab - 12 GeV Upgrade will greatly enhance our

capability - Goal a full understanding of nucleon structure

and strong interaction